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Inexact proximal DC Newton-type method for nonconvex composite functions

Author

Listed:
  • Shummin Nakayama

    (The University of Electro-Communications)

  • Yasushi Narushima

    (Keio University)

  • Hiroshi Yabe

    (Tokyo University of Science)

Abstract

We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possibly nonsmooth DC function. The application of proximal DC algorithms to address this problem class is well-known. In this paper, we combine a proximal DC algorithm with an inexact proximal Newton-type method to propose an inexact proximal DC Newton-type method. We demonstrate global convergence properties of the proposed method. In addition, we give a memoryless quasi-Newton matrix for scaled proximal mappings and consider a two-dimensional system of semi-smooth equations that arise in calculating scaled proximal mappings. To efficiently obtain the scaled proximal mappings, we adopt a semi-smooth Newton method to inexactly solve the system. Finally, we present some numerical experiments to investigate the efficiency of the proposed method, which show that the proposed method outperforms existing methods.

Suggested Citation

  • Shummin Nakayama & Yasushi Narushima & Hiroshi Yabe, 2024. "Inexact proximal DC Newton-type method for nonconvex composite functions," Computational Optimization and Applications, Springer, vol. 87(2), pages 611-640, March.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:2:d:10.1007_s10589-023-00525-9
    DOI: 10.1007/s10589-023-00525-9
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    References listed on IDEAS

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    1. Shummin Nakayama & Yasushi Narushima & Hiroshi Yabe, 2021. "Inexact proximal memoryless quasi-Newton methods based on the Broyden family for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 79(1), pages 127-154, May.
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    3. Zhaosong Lu & Xiaorui Li, 2018. "Sparse Recovery via Partial Regularization: Models, Theory, and Algorithms," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1290-1316, November.
    4. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    5. Jinchao Li & Martin S. Andersen & Lieven Vandenberghe, 2017. "Inexact proximal Newton methods for self-concordant functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 19-41, February.
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